Swaying hoisted load-piece damping control apparatus

ABSTRACT

A transverse trolley  11  is transversally movable on a crane girder. A driver is provided for the transverse trolley  11 . A pair of sheave blocks  14, 15  which is movable relative to a transverse trolley  11  are disposed on both (right and left) sides of a transverse trolley  11 . Drivers are provided for the sheave blocks. Detectors  31  through  38  are provided which detect the displacement and velocity of the transverse trolley  11 , the sway displacement and velocity of a hoisted load-piece  23  on both (right and left) sides and the displacement and velocity of the two sheave blocks  14, 15 . A notch is disposed on an operation controlling panel of the transverse trolley  11  for setting a trolley transverse velocity by an operator. A transverse notch-driving control quantity detector  40  is provided which outputs signals indicative of notch-driving control quantity (a trolley transverse velocity set value) which is set by operating the notch. A controller is provided which effects sway-damping control of the load-piece hoisting device based on detection signals obtained from the detectors  31  through  38  and  40 , and an optimizing control unit performs sway-damping control with optimal controlling quantities on the basis of a preset optimal gain K in accordance with the displacement and velocity and the notch-driving control quantity.

This application is a divisional and continuation-in-part of applicationSer. No. 08/948,122 filed Oct. 9, 1997 which is a continuation-in-partof application Ser. No. 08/412,299 filed Mar. 28, 1995 now abandoned.

FIELD OF THE INVENTION AND RELATED ART STATEMENT

(1) Field of the Invention

The present invention relates to a swaying hoisted load-piece dampingcontrol apparatus, and more detailedly relates to a swaying hoistedload-piece damping control apparatus for a load-piece hoisting deviceused in a large-scale load-piece lifting container crane and the like.

(2) Description of the Prior Art

FIG. 6 shows an overall configuration of a swaying hoisted load-piecedamping apparatus for use in a conventional container crane and FIG. 7shows operating states of the conventional swaying hoisted load-piecedamping apparatus.

As shown in FIG. 6, a transverse trolley 11 is provided transversallymovable (movable in the side-to-side directions in FIG. 6 on main cranegirder 29. The transverse trolley 11 has a pair of rails 12 and 13thereon which guide a pair of sheave blocks 14 and 15, respectively sothat the sheave blocks 14 and 15 can move within short range in parallelwith the moving direction of the transverse trolley 11. The transversetrolley 11 is connected through a wire 16 to a trolley driver 17disposed on the main girder (not shown) on which the transverse trolley11 moves. The sheave blocks 14 and 15 have respective sheave blockdrivers 18 and 19 for driving the sheave blocks 14 and 15. A hoistingattachment 22 is hanged from the transverse trolley 11 through windingwires 20. This hoisting attachment 22 hoists a container 23 as a hoistedload-piece. Here, as shown in FIG. 6, the hoisting attachment 22 has adetecting mark 21 for detecting the sway of the hoisted load-piece onthe upper surface thereof.

In stopping the sway of such a load-piece hoisting device, the operatorin the operator cab, visually observing the motion of the hoistingattachment 22, used to perform manual remote-control operations in thefollowing manner.

That is, in the state shown in FIG. 6, when the trolley drivers 17drives the transverse trolley 11 from the left to the right in adirection shown by an arrow α, if the movement of the transverse trolley11 is changed from the constant-speed transverse travel mode to theretarding travel mode, the hoisted load-piece 23 hanged by the hoistingattachment 22 sways rightward (forward) due to its inertia, as indicatedby an arrow β in FIG. 7(a). At that moment, as the operator in theoperator cab watches the detecting mark 21 on the hoisting attachment 22and perceives the sway, the operator controls the transverse trolley 11to accelerate as indicated by an arrow α in FIG. 7(b), in conformitywith the transverse sway of the hoisted load-piece 23 (in theaforementioned direction of the arrow α). Alternatively, the two sheaveblocks 14, 15 may be controlled to move in the same direction with theswaying direction of the hoisted load-piece 23 by activating the leftand right sheave block drivers 18, 19 on the transverse trolley 11.Thereafter, the operator tries to control the transverse trolley 11 toretard in time with the reverse motion of the hoisted load-piece 23after the trolley completes a rightward (forward)-swing of a certainmagnitude or should control the sheave blocks 14, 15 to move in theopposite direction to the aforementioned direction so that thetransversally swinging load-piece is dampened to stop.

In the case shown in FIG. 6, if, for example, the hoisted load-piece 23slues clockwise causing skew sway on a plane as indicated by arrows A,the operator again perceives it from the movement of the detecting mark21 and activates the driver 18, 19 so as to move the sheave block 15leftward (in the direction shown by an arrow B) and the other sheaveblock 14 rightward (in the direction shown by an arrow C) in synchronismwith the skew sway. To deal with a repulsive swing of the hoistedload-piece 23, the sheave blocks 14, 15 may and should be driven in theopposite directions to those described above, so that the skew sway isattenuated to stop.

The conventional, swaying hoisted load-piece damping apparatus in whichsway is manually stopped by the operator, however, suffers from problemsas follows.

That is, as stated above, it is true that simple transverse sway orsimple skew sway of the hoisted load-piece 23 can be attenuated andstopped by the operator by accelerating and/or retarding the transversetrolley 11 or by moving the sheave blocks 14,15 in synchronism with theswinging state of the hoisting attachment 22. But, if transverse swayand skew sway occur at the same time and cause the hoisted load-piece 23to make a complex motion, it becomes difficult or practically impossiblefor the operator to manually drive the transverse trolley 11 or thesheave blocks 14, 15 well enough to deal with the situation.

As soon as the hoisted load-piece 23 is stopped to sway, the sheaveblocks must normally be returned by force to their home positions or themiddle of the transverse trolley 11 with respect to the transversedirection, so that the two (left and right) sheaves 14 and 15 can movein either transverse direction to prepare for a next swing of thehoisted load-piece 23. In order to improve the efficiency of conveyingthe hoisted load-piece 23, the transverse trolley 11 must be driven at amaximum speed during it travels transversally. When the hoistedload-piece 23 comes near a target position where it is to be unloadedonto the ground, the transverse trolley 11 should be retarded so as tostop at the target position and then need be stopped at the targetposition where the load-piece is unloaded. To sum up, it is necessary toeffect, all at once, position control of the sheave blocks 14 and 15,velocity and/or position control of the transverse trolley 11 inconformity with the transverse position and conditions, other than thecontrol of damping the swaying hoisted load-piece 23. Nevertheless,since the conventional sway-damping operation is manually effected bythe operator, the controlling operation requires the toughest techniquesfor even the skilled operators.

OBJECT AND SUMMARY OF THE INVENTION

The present invention has been achieved to solve the above problems andit is therefore an object of the present invention to provide a swayinghoisted load-piece damping control apparatus which simplifies theoperation of damping swaying hoisted load-piece and is able to achievethe damping operation in an assured manner.

Another object of the present invention is to provide a swaying hoistedload-piece damping control apparatus which is able to realize an optimalcontrol for damping and stopping a swaying hoisted load-piece as fast aspossible by automating the complicated swaying hoisted load-piecedamping operation.

A further object of the present invention is to provide a swayinghoisted load-piece damping control apparatus which is able to improvethe work efficiency of conveying hoisted load-pieces by markedlyreducing the work amount of the operator and the time required for swaydamping.

In order to attain the above objects, a swaying hoisted load-piecedamping control apparatus (an apparatus defined in claim 1) for use in aload-piece hoisting device having a transverse trolley for hoisting aload-piece being transversally movable on a crane girder and the driverthereof, and a pair of, or right and left, sheave blocks which aredisposed along moving directions of said transverse trolley in parallelwith the sides of said transverse trolley and movable relative to saidtransverse trolley and the drivers thereof, comprises: trolleydisplacement/velocity detectors for detecting a displacement and avelocity of said transverse trolley; sway detectors for detecting thedisplacement and velocity of a sway on right and left sides of theload-piece hoisted by said transverse trolley; sheave-blockdisplacement/velocity detectors for detecting the displacement andvelocity of said right and left sheave blocks; a notch disposed on anoperation controlling panel of said transverse trolley, for setting atrolley transverse velocity by an operator; a notch-driving operationquantity detector for outputting signals indicative of notch-drivingoperation quantity (a trolley transverse velocity set value) which isset by operating said notch; and a controller for effecting sway-dampingcontrol of said load-piece hoisting device based on detection signalsobtained from said detectors, characterized in that said controller hasan optimizing control unit which sets up optimal controlling quantitiesfor the hoisted load-piece in accordance with the displacement andvelocity and notch-driving operation quantity detected from saiddetectors, on the basis of a preset optimal gain for sway damping, andperforms sway-damping control by driving said transverse trolley andsaid sheave blocks in accordance with the setup optimal controllingquantities.

According to the present invention, in the swaying hoisted load-piecedamping control apparatus defined in claim 1, the controller comprises:an operating condition determining unit which detects the operatingcondition of the transverse trolley, based on the displacement andvelocity and the notch-driving operation quantity for said transversetrolley; an operating-condition-classifying optimal-gain selecting unitwhich, in accordance with the operating condition detected by theoperating condition determining unit, selects anoperating-condition-classifying optimal gain for sway damping from aplurality of predetermined optimal gains; and an optimizing control unitwhich, based on the optimal gain outputted from theoperating-condition-classifying optimal-gain selecting unit, sets upoptimal controlling quantities for the hoisted load-piece and performssway-damping control by driving the transverse trolley and the sheaveblocks in accordance with the setup optimal controlling quantities.

According to the present invention, in the swaying hoisted load-piecedamping control apparatus defined in claim 1, the controller comprises:an independently controlling optimal-gain calculating unit which drivessaid transverse trolley and said sheave blocks so as to damp transversesway and skew sway, respectively, that is, calculates independentoptimal gains used to control transverse sway and skew sway of thehoisted load-piece, independently one from the other by separate driversand outputs the calculated optimal gains; and an optimizing control unitfor effecting sway-damping control which, based on the optimal gainsoutputted from said independently controlling optimal-gain calculatingunit, sets up optimal controlling quantities for hoisted load-piece andperforms sway-damping control by driving said transverse trolley to damptransverse sway of the load-piece and driving said right and left sheaveblocks to damp skew sway of the load-piece.

According to the present invention, in the swaying hoisted load-piecedamping control apparatus defined in claim 1, the controller comprises:an independently controlling optimal-gain calculating unit whichcalculates independent optimal gains used to control transverse sway andskew sway of the hoisted load-piece, independently one from the otherand outputs the calculated optimal gains; an operating conditiondetermining unit which detects the operating condition of the transversetrolley, based on the displacement and velocity and the notch-drivingoperation quantity for said transverse trolley; anoperating-condition-classifying optimal-gain selecting unit which, inaccordance with the operating condition detected by the operatingcondition determining unit, selects a presetoperating-condition-classifying optimal gain or anoperating-condition-classifying optimal gain set up by the independentlycontrolling optimal-gain calculating unit and outputs the selected gain;and an optimizing control unit which, based on the optimal gainoutputted from the operating-condition-classifying optimal-gainselecting unit, sets up optimal controlling quantities for the hoistedload-piece and performs sway-damping control by driving the transversetrolley and the sheave blocks in accordance with the setup optimalcontrolling quantities.

In accordance with the swaying hoisted load-piece damping controlapparatus of the present invention, as the container crane is activated,detection signals are detected by the transverse trolleydisplacement/velocity detectors, the right-and-left-sheave-blockdisplacement/velocity detectors, the hoisted load-piece sway detectorsfor detecting the sway on right and left sides of the load-piece and thenotch-driving operation quantity detector. The thus detected signals aresent to the controller. In the controller, an optimal gain for swaydamping is previously determined, and then the optimizing control uniteffects sway-damping control by driving the transverse trolley and thesheave blocks by optimal controlling quantities calculated on the basisof the optimal gain and the signals detected by the detectors.

The operating condition determining unit, based on the signals from thetransverse trolley displacement/velocity detectors and from thenotch-driving operation quantity detector, determines which conditionthe transverse trolley is in, specifically, the condition in which thetransverse trolley travels, the condition in which the trolley isretarded for positioning or the condition in which the trolley isstopped with the hoisted load-piece swaying alone. The determined signalis outputted to the operating-condition-classifying optimal gainselecting unit. This operating-condition-classifying optimal gainselecting unit, as receiving the determine signal, selects any one ofoptimal gains previously set up according to plural classifyingoperating conditions and outputs the thus selected optimal gain to theoptimizing control unit. The optimizing control unit sets up an optimalcontrolling quantity calculated on the basis of the selected optimalgain and the signals detected by the detectors and drives the transversetrolley and the sheave blocks by the thus set up by optimal controllingquantities, to thereby perform sway-damping control.

The independently controlling optimal gain calculating unit calculatesan optimal gain which realizes a task allocation of the transversetrolley and the sheave blocks, namely, drives the transverse trolley andthe sheave blocks for damping transverse sway and skew sway of thehoisted load-piece, respectively, so as to output it to the optimizingcontrol unit. The optimizing control unit effects sway-damping controlby driving the transverse trolley and the sheave blocks by the optimalcontrolling quantity calculated on the basis of the optimal gain and thesignals detected by the detectors.

The independently controlling optimal gain calculating unit calculatesan optimal gain which realizes the task allocation of the transversetrolley and the sheave blocks, namely, drives the transverse trolley andthe sheave blocks for damping transverse sway and skew sway of thehoisted load-piece, respectively, so as to output it to theoperating-condition-classifying optimal gain selecting unit while theoperating condition determining unit, based on the signals from thetransverse trolley displacement/velocity detectors and from thenotch-driving operation quantity detector, determines which conditionthe transverse trolley is in, specifically, the condition in which thetransverse trolley travels, the condition in which the trolley isretarded for positioning or the condition in which the trolley isstopped with the hoisted load-piece swaying alone and outputs thedetermined signal to the operating-condition-classifying optimal gainselecting unit. The operating-condition-classifying optimal gainselecting unit, as receiving these determined signals, selects one ofthe optical gains classified according to the operating condition andoutputs it as an optical gain to the optimizing control unit. Theoptimizing control unit effects sway-damping control by driving thetransverse trolley and the sheave blocks by the optimal controllingquantity calculated on the basis of the optimal gain and the signalsdetected by the detectors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic constructional view showing an overallconfiguration of a swaying hoisted load-piece damping control apparatusin accordance with an embodiment of the present invention;

FIG. 2 is a block diagram showing a first embodiment of a controllingapparatus;

FIG. 3 is a block diagram showing a second embodiment of a controllingapparatus;

FIG. 4 is a block diagram showing a third embodiment of a controllingapparatus;

FIG. 5 is a block diagram showing a fourth embodiment of a controllingapparatus;

FIG. 6 is a schematic view showing a conventional swaying hoistedload-piece damping apparatus for use in a prior art container crane;

FIGS. 7a and b show illustrations of operating conditions of theconventional swaying hoisted load-piece damping apparatus;

FIG. 8 is a block diagram showing an optimizing control unit of thefirst through fourth embodiments of the controlling apparatus; and

FIG. 9 shows an equivalent model relative to a transverse trolley, leftand right sheave blocks and swinging motions on the right and left sidesof the hoisted load-piece for deriving a required state equation fordetermining an optical gain.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the present invention will hereinafter be described indetail with reference to FIGS. 1 through 5.

FIG. 1 schematically shows an overall configuration of a swaying hoistedload-piece damping control apparatus in accordance with an embodiment ofthe present invention. FIG. 2 is a controlling block for explaining afirst embodiment of a controlling apparatus. In FIG. 1, identicalreference numerals are allotted to components having the same functionswith those in the prior art shown in FIG. 6 and repeated description forthose is omitted.

As shown in FIG. 1, in a controlling apparatus for damping a swayinghoisted load-piece of this embodiment, the trolley driver 17 of thetransverse trolley 11 includes a position or displacement detector 31and a velocity detector 32 for the trolley. The left-side sheave block14 is provided with a displacement detector 33 and a velocity detector34 for the sheave blocks. In the same manner, the right-side sheaveblock 15 is provided with a displacement detector 35 and a velocitydetector 36. In order to detect sway of the hoisted load-piece, swaydetectors 37, 38 and provided respectively on left and right sides ofthe traverse trolley 11 so as to check the motion of the detecting mark21 on the hoisting attachment 22 and thereby detect left-side andright-side swaying displacements and velocities of the hoistedload-piece 23.

A traverse operation controlling panel 39 in the crane operator cabincludes a gear shift lever in a notch for setting a trolley traversevelocity by changing gear settings. A notch-driving operation quantitydetector 40 outputs signals indicative of a notch-driving operationquantity that the operator sets up by operating the gear shift lever.The detector 40 detects integral values “0”, “1”, “2” . . . asnotch-driving operation quantities. Each value corresponds to a gearselection (i.e. neutral gear (“0”), low gear (“1”), second gear (“2”)).

Each of the detectors will be described below.

Motors are used as the drivers for the traverse trolley and right andleft sheave blocks. For the traverse trolley, the motor rotates a drumaround which a wire 16 is wound so as to wind up or off the wire,thereby allowing the traverse trolley to traversely move on a cranegirder. For the sheave blocks, the motor rotates a ball screw so as toslide the sheave blocks on the ball screw. Here, a rotating angle and arotating velocity of the motor are proportional to a motion displacementand a motion velocity of the traverse trolley and sheave blocks.

On the other hand, the commercially-available motor is equipped with anencoder for detecting the rotating angle and a pulse generator fordetecting the rotating-angle velocity so that the rotating angle and therotating-angle velocity can be detected.

In the transverse trolley and left and right sheave blocks, the signals,which are detected by the encoder and pulse generator attached to eachmotor, are therefore proportional signal to the motion displacement andvelocity. That is, these are detectors for detecting the displacementand velocity of the transverse trolley and left and right sheave blocks.

A sway detector comprises a CCD camera and an image processingapparatus. The detecting mark on the hoisting attachment is picked up bythe CCD camera. The mark is then transmitted to the image processingapparatus as an image signal whose luminance is changed by a certainpixel. In the image processing apparatus, an image signal luminancechange position is detected so as to detect a mark position, that is,sway displacement. The sway displacement is calculated during theinterval between the previous time and the current time so as to detecta sway velocity.

A controller 41 is to receive detection signals x₀, *x₀, x₁, *x₁, x₂,*x₂, d₁, *d₁, d₂, *d₂ and v₀ from all the detectors 31 through 38 andthe notch-driving operation quantity detector 40 . The controller 41 isalso to calculate, based on an optimal gain /K for sway damping which ispreviously calculated and set up separately in the controller as shownin FIG. 2, optimal controlling quantities required for moving thetransverse trolley as the operator's notch operation and for stoppingthe sway of the hoisted load-piece 23. The controller 41 is further tooutput the optimal controlling quantities as control command signals tothe driver 17 for the transverse trolley 11 and the drivers 18, 19 forleft and right sheave blocks 14, 15.

Now, description will be made on a specific operational process of swaydamping using the swaying hoisted load-piece damping control apparatusof the embodiment described above.

(1) First of all, detectors 31 through 38 and 40 detect the displacementand velocity of the transverse trolley 11, the sheave blocks 14, 15 andthe hoisted load-piece 23 and a notch-driving operation quantity andoutput the detected signals to the controller 41.

(2) Next, these displacement and velocity and notch-driving operationquantity v₀ are used in the optimizing control unit 42 for calculationof optimal sway-damping control to calculate a velocity command u₀ forthe transverse trolley 11 and velocity commands u₁, u₂ for the sheaveblocks 14, 15 by the following formula [1] as shown in FIG. 8:

/K=/K(x−x_(r))

x_(r)=G₁v₀  [1]

Here, /u represents a controlling (operating) quantity vector shown asfollows and the elements are the velocity command u₀ for the transversetrolley 11, the velocity command u₁ for the left-side sheave block 14and the velocity command u₂ for the right-side sheave block 15, in orderfrom the left, and more explicitly, /u can be defined as the followingequation [2]:

 /u=[u₀ u₁ u₂]^(T)  [2]

A condition quantity vector /x is defined as follows. That is, theelements are, in order from the left, a displacement x₀ and a velocity*xof the transverse trolley 11, a displacement x₁ and a velocity *x₁ ofthe left sheave block 14, a displacement x₂ and a velocity *x₂ of theright sheave block 15, a displacement d₁ and a velocity *d₁ of thehoisted load-piece 23 on its left side, and a displacement d₂ and avelocity *d₂ of the hoisted load-piece 23 on its right side. Explicitly,/x can be expressed as the following equation [3]:

/x=[x₀ {dot over (x)}₀x₁ {dot over (x)}₁ x₂ {dot over (x)}₂ d₁ {dot over(d)}₁ d₂ {dot over (d)}_(2]) ^(T)  [3]

/xr is a vector as described below. The second element from the left isthe notch-driving operation quantity v₀. The other elements are equal tozero. /xr is given by multiplying a constant vector G₁ described belowby the notch-driving operation quantity v₀ that is one of input signals.$\begin{matrix}\left. \begin{matrix}{_{r} = \left\lbrack {0\quad v_{0}\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack^{T}} \\{_{1} = \left\lbrack {0\quad 1\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack^{T}}\end{matrix} \right\} & \lbrack 4\rbrack\end{matrix}$

A 3×10 constant matrix /K defined by the following equation representsan optimal gain matrix: $\begin{matrix}{ = \begin{bmatrix}k_{00} & k_{01} & k_{02} & k_{03} & k_{04} & k_{05} & k_{06} & k_{07} & k_{08} & k_{09} \\k_{10} & k_{11} & k_{12} & k_{13} & k_{14} & k_{15} & k_{16} & k_{17} & k_{18} & k_{19} \\k_{20} & k_{21} & k_{22} & k_{23} & k_{24} & k_{25} & k_{26} & k_{27} & k_{28} & k_{29}\end{bmatrix}} & \lbrack 6\rbrack\end{matrix}$

Here, the constant matrix /K as an optimal gain is to be calculatedpreviously by the following procedures.

1) FIG. 9 shows an equivalent model for the transverse trolley 11, thetwo (left and right) sheave blocks 14, 15 and swinging motions on theright and left sides of the hoisted load-piece 23.

Here, a pendulum motion of the hoisted load-piece is similar to a springmotion. An equivalent spring constant k is expressed by the equationk=mg/(21) from a wire length l and a mass of hoisted load-piece m. Fromthe equivalent model, the following equations of motion can be derived:$\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{M_{0}{\overset{¨}{x}}_{0}} = {f_{0} - f_{1} - f_{2}}} \\{{M_{1}\left( {{\overset{¨}{x}}_{0} + {\overset{¨}{x}}_{1}} \right)} = {f_{1} + {k\left( {d_{1} - x_{1}} \right)}}}\end{matrix} \\{{M_{2}\left( {{\overset{¨}{x}}_{0} + {\overset{¨}{x}}_{2}} \right)} = {f_{2} + {k\left( {d_{2} - x_{2}} \right)}}}\end{matrix} \\{{m\left\lbrack {{\overset{¨}{x}}_{0} + {\left( {{\overset{¨}{d}}_{1} + {\overset{¨}{d}}_{2}} \right)/2}} \right\rbrack} = {{- {k\left( {d_{1} - x_{1}} \right)}} - {k\left( {d_{2} - x_{2}} \right)}}}\end{matrix} \\{{I\quad \overset{¨}{\psi}} = {{k\left\lbrack {\left( {d_{2} - x_{2}} \right){r/2}} \right\rbrack} - {{k\left( {d_{1} - x_{i}} \right)}{r/2}}}}\end{matrix} \\{\overset{¨}{\psi} = {\left( {d_{1} - d_{2}} \right)/r}}\end{matrix} \right\} & \lbrack 7\rbrack\end{matrix}$

Here, M₀ denotes a mass of trolley. M₁ and M₂ denote masses of left andright sheaves, respectively. m denotes a mass of hoisted load-piece. Idenotes moment of inertia of hoisted load-piece. x₀ denotes a trolleyposition. x₁ and x₂ denote positions of left and right sheaves. d₁ andd₂ denote sway widths of hoisted load-piece on the left and right sides.ψ denotes a skew angle. γ denotes a length of hoisted load-piece. f₀denotes a trolley drive force. f₁ and f₂ denote drive forces of left andright sheaves.

From the equations of motion expressed by the equation [7], a stateequation is derived where a state vector x=[x₀ x*₀ x₁* x₁ x₂ *x₂ d₁ *d₁d₂ *d₂]^(r), which is expressed by the following equation [8]:

{dot over (x)}=Âx+{circumflex over (B)}f  [8]

where Â and {circumflex over (B)} are expressed by the followingequation [9]: $\begin{matrix}\left. \begin{matrix}{\hat{A} = \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {- \frac{K}{M_{1}}} & 0 & 0 & 0 & \frac{K}{M_{1}} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {- \frac{K}{M_{2}}} & 0 & 0 & 0 & \frac{K}{M_{2}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & {\frac{K}{m} + \frac{{Kr}^{2}}{4I}} & 0 & {\frac{K}{m} - \frac{{Kr}^{2}}{4I}} & 0 & {- \left( {\frac{K}{m} + \frac{{Kr}^{2}}{4I}} \right)} & 0 & {- \left( {\frac{K}{m} - \frac{{Kr}^{2}}{4I}} \right)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & {\frac{K}{m} - \frac{{Kr}^{2}}{4I}} & 0 & {\frac{K}{m} + \frac{{Kr}^{2}}{4I}} & 0 & {- \left( {\frac{K}{m} - \frac{{Kr}^{2}}{4I}} \right)} & 0 & {- \left( {\frac{K}{m} + \frac{{Kr}^{2}}{4I}} \right)} & 0\end{bmatrix}} \\{\hat{B} = \begin{bmatrix}0 & 0 & 0 \\\frac{1}{M_{0}} & {- \frac{1}{M_{0}}} & {- \frac{1}{M_{0}}} \\0 & 0 & 0 \\{- \frac{1}{M_{0}}} & {\frac{1}{M_{1}} + \frac{1}{M_{0}}} & \frac{1}{M_{0}} \\0 & 0 & 0 \\{- \frac{1}{M_{0}}} & \frac{1}{M_{0}} & \frac{1}{M_{0}} \\0 & 0 & 0 \\{- \frac{1}{M_{0}}} & \frac{1}{M_{0}} & \frac{1}{M_{0}}\end{bmatrix}}\end{matrix} \right\} & \lbrack 9\rbrack\end{matrix}$

Here, the state vector and drive force vector are represented by thefollowing equation [10]: $\begin{matrix}{x = {{\begin{bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}x_{0} \\x_{0}\end{matrix} \\x_{1}\end{matrix} \\x_{1}\end{matrix} \\x_{2}\end{matrix} \\x_{2}\end{matrix} \\d_{1}\end{matrix} \\d_{1}\end{matrix} \\d_{2}\end{matrix} \\d_{2}\end{bmatrix}\quad f} = \begin{bmatrix}\begin{matrix}f_{0} \\f_{1}\end{matrix} \\f_{2}\end{bmatrix}}} & \lbrack 10\rbrack\end{matrix}$

On the other hand, the operation quantities of the transverse trolleyand the left and right sheave blocks are indicative of the velocitycommands u₀, u₁ and u₂. In a velocity controlling system configuration,the following relationship is represented between these velocitycommands and the drive forces f₀, f₁ and f₂ applied to the transversetrolley and the left and right sheave blocks: $\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{the}\quad {transverse}\quad {trolley}} \\{f_{0} = {{K_{p0}\left( {u_{0} - {\overset{.}{x}}_{0}} \right)} - {M_{0}^{\prime}{\overset{¨}{x}}_{0}}}}\end{matrix} \\{{the}\quad {left}\quad {and}\quad {right}\quad {sheave}\quad {blocks}}\end{matrix} \\{f_{1} = {{K_{p1}\left( {u_{1} - {\overset{.}{x}}_{1}} \right)} - {M_{1}^{\prime}{\overset{¨}{x}}_{1}}}}\end{matrix} \\{f_{2} = {{K_{p2}\left( {u_{2} - {\overset{.}{x}}_{2}} \right)} - {M_{2}^{\prime}{\overset{¨}{x}}_{2}}}}\end{matrix} \right\} & \lbrack 11\rbrack\end{matrix}$

Here, K_(p0) denotes a velocity control gain for a trolley drive motor.K_(p1) and K_(p2) denote velocity control gains for the drive motors ofthe left and right sheave blocks, respectively. M₀′ denotes a reducedmass value of moment of inertia of the trolley drive motor. M₁′ and M₂′denote reduced mass values of moment of inertia of the left and rightsheave blocks, respectively.

Here, the vector of the operation quantities is expressed by thefollowing equation [12]: $\begin{matrix}{u = \begin{bmatrix}\begin{matrix}u_{0} \\u_{1}\end{matrix} \\u_{2}\end{bmatrix}} & \lbrack 12\rbrack\end{matrix}$

The following equation [13] indicates the relationship between thevelocity commands and drive forces:

f=H₁ {dot over (x)}+H₂ x+H₃ u  [13]

where coefficient matrices H₁, H₂ and H₃ are expressed by the followingequation [14]: $\begin{matrix}\left. \begin{matrix}\begin{matrix}{H_{1} = \begin{bmatrix}0 & {- M_{0}^{\prime}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {- M_{1}^{\prime}} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {- M_{2}^{\prime}} & 0 & 0 & 0 & 0\end{bmatrix}} \\{H_{2} = \begin{bmatrix}0 & {- K_{p0}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {- K_{p1}} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {- K_{p2}} & 0 & 0 & 0 & 0\end{bmatrix}}\end{matrix} \\{H_{3} = \begin{bmatrix}K_{p0} & 0 & 0 \\0 & K_{p1} & 0 \\0 & 0 & K_{p1}\end{bmatrix}}\end{matrix} \right\} & \lbrack 14\rbrack\end{matrix}$

The equation [8] is the equation of state of the transverse trolley, theleft and right sheave blocks and the swinging motions on the right andleft sides of hoisted load-piece. The equation [13] is a determinantwhich is indicative of motor velocity controlling systems of thetransverse trolley and the left and right sheave blocks. The equation[8] and the equation [13] are combined with each other so as to beintegrated. This results in the state equation where the velocitycommands are defined as the operation quantities, which is expressed bythe following equation [15]: $\begin{matrix}\left. \begin{matrix}{\overset{.}{} = {{\hat{}} + {\hat{}\left( {{_{1}\overset{.}{}} + {_{2}} + {_{3}}} \right)}}} \\{\overset{.}{} = {{\left( { - {\hat{}\quad _{1}}} \right)^{- 1}\left( {\hat{} + {\hat{}\quad _{2}}} \right)} + {\left( { - {\hat{}\quad _{1}}} \right)^{- 1}\hat{\quad}_{3}}}}\end{matrix} \right\} & \lbrack 15\rbrack\end{matrix}$

where II denotes a 10×10 unit matrix.

When A and B matrices are defined in the following manner, the stateequation is represented by the following equation [16]: $\begin{matrix}\left. \begin{matrix}\begin{matrix}{ = {\left( { - {\hat{}\quad _{1}}} \right)^{- 1}\left( {\hat{} + {\hat{}\quad _{2}}} \right)}} \\{ = {\left( { - {\hat{}\quad _{1}}} \right)^{- 1}\hat{}\quad _{3}}}\end{matrix} \\{= { + }}\end{matrix} \right\} & \lbrack 16\rbrack\end{matrix}$

2) Next, an evaluation function J is set up. $\begin{matrix}\left. \begin{matrix}\begin{matrix}{J = {\int_{0}^{\infty}{\left( {{x^{T}{Qx}} + {u^{T}{Ru}}} \right)\quad {t}}}} \\{Q = {{diag}\quad \left( {q_{1}\quad q_{2}\quad q_{3}\quad q_{4}\quad q_{5}\quad q_{6}\quad q_{7}\quad q_{8}\quad q_{9}\quad q_{10}} \right)}}\end{matrix} \\{R = {{diag}\quad \left( {r_{1}\quad r_{2}\quad r_{3}} \right)}}\end{matrix} \right\} & \lbrack 17\rbrack\end{matrix}$

Weighing matrices Q and R are composed of each element which means asfollows:

q₁, q₂: weighing coefficients relative to the trolley position andvelocity;

q₃, q₄: weighing coefficients relative to the displacement and velocityof the left sheave block;

q₅, q₆: weighing coefficients relative to the displacement and velocityof the right sheave block;

q₇, q₈: weighing coefficients relative to the sway displacement andvelocity of the hoisted load-piece at the left end;

q₉, q₁₀: weighing coefficients relative to the sway displacement andvelocity of the hoisted load-piece at the right end;

r₁: weighing coefficient relative to the trolley velocity command;

r₂: weighing coefficient relative to the left sheave block velocitycommand; and

r₃: weighing coefficient relative to the right sheave block velocitycommand.

Values of weighing coefficients are set in the following manner.

q₁ through q₁₀ are to designate a strength of control. For example, whenthe control for sway damping of the hoisted load-piece is strengthened,q₇ through q₁₀ are set to larger values.

r₁ through r₃ are to limit the velocity commands of the transversetrolley and the left and right sheave blocks. For example, when a strictlimitation is imposed on the trolley velocity command, r₁ is set to thelarger value.

These values are adjusted while performing an actual machine test.

3) On the basis of the aforementioned state equation [16], the optimalgain K for minimizing the evaluation function [17] can be determined bythe following equation [18]:

K=−R⁻¹B^(T)P  [18]

where P represents an algebraic matrix Riccati's equation and is apositively symmetric solution of the following equation [19]:

A^(T)P+PA−PBR⁻¹B^(T)P+Q=0  [19]

(3) The velocity commands u₀, u₁ and u₂ determined by the equation [1]are outputted to the drivers 17, 18 and 19 of the transverse trolley 11and the left and right sheave blocks 14 and 15, respectively, as thecontrol command signals. These drivers are activated so as to effect theoptimal control for sway damping of the hoisted load-piece 23.

FIG. 3 shows a controlling block representing a second embodiment of aswaying hoisted load-piece damping control apparatus of the presentinvention.

As shown in FIG. 3, in this embodiment, a controller 51 is composed of:an operating condition determining unit 52 which, receiving detectedsignals from a notch-driving operation quantity detector 40, trolleydisplacement and velocity detectors 31 and 32, determines the operatingcondition of a transverse trolley 11 or which condition the transversetrolley 11 is in, specifically, a condition in which the trolley 11 isdriven, a condition in which the trolley 11 is in the middle ofretardation to stop at a target place or a condition in which thetrolley 11 need sway damping after the positioning, to thereby deliveroutput signals; an operating-condition-classifying optimal-gainselecting unit 53 which, based on the signals from the operatingcondition determining unit 52 and a plurality ofoperating-condition-classifying optimal gains /K₁, /K₂ and /K₃ which arepreviously calculated and set up for the different operating conditions,selects an optimal gain /K for the detected operating condition from theoperating-condition-classifying optimal gains /K₁, /K₂ and /K₃; and anoptimizing control unit 54 which, receiving the optimal gain /K selectedin the operating-condition-classifying optimal-gain selecting unit 53,calculates and sets up optimal controlling quantities in accordance withthe detection signals inputted from the detectors 31 through 38 and 40and outputs the optimal controlling quantities as control commandsignals to the drivers 17 of the transverse trolley 11, the drivers 18,19 of respective (left and right) sheave blocks 14, 15.

Now, description will be made on a specific sway-damping processeffected by the controller 51 of this embodiment.

(1) The operating condition determining unit 52 determines the operatingcondition of the transverse trolley 11 based on the detected signalsfrom the notch-driving operation quantity detector 40, the trolleydisplacement and velocity detectors 31, 32. At that moment, if theoperator is performing a notch-driving operation or the notch-drivingoperation quantity is not zero, the unit 52 judges that the hoistedload-piece 23 is still far from a target position where the load-pieceis to be placed on the ground. When the notch-driving operation quantitybecomes equal to zero, the unit 52 judges that the load-piece comes nearthe target position. When the notch-driving operation quantity is equalto zero and the transverse trolley displacement information indicatesthat the load-piece 23 is at the target position with the transversevelocity equal to zero, the hoisted load-piece 23 is judged as to reachthe target position.

(2) The operating-condition-classifying optimal-gain selecting unit 53selects as the optimal gain /K any one of three optimal gains /K₁, /K₂and /K₃ in accordance with the operating condition determined in (1).Here, the optimal gains /K₁, /K₂ and /K₃ are determined in the samemanner as in the first embodiment. That is, on the basis of the stateequation [16] derived from 1) of (2) described in the first embodiment,the equations [18] and [19] in 3) are solved so as to previouslydetermine the optimal gain /K for minimizing the evaluation function[17] which is set up in 2). It should be noted that the evaluationfunction J is expressed by the following three evaluation functions J₁,J₂ and J₃. In the evaluation function J, the optimal gains are /K₁, /K₂and /K₃ corresponding to the evaluation functions J₁, J₂ and J₃,respectively. $\begin{matrix}\left. \begin{matrix}\begin{matrix}{J_{1} = {\int_{0}^{\infty}{\left( {{x^{T}Q_{1}x} + {u^{T}R_{1}u}} \right)\quad {t}}}} \\{J_{2} = {\int_{0}^{\infty}{\left( {{x^{T}Q_{2}x} + {u^{T}R_{2}u}} \right)\quad {t}}}}\end{matrix} \\{J_{3} = {\int_{0}^{\infty}{\left( {{x^{T}Q_{3}x} + {u^{T}{Ru}}} \right)\quad {t}}}}\end{matrix} \right\} & \lbrack 20\rbrack\end{matrix}$

Here, /Q₁ and /R₁ are weighing matrices, wherein the first element isequal to zero from the left in the weighing coefficient /Q₁ (relative tothe trolley position, for a velocity following type optimal-gaincalculation mode in which the operator effects notch-driving operationin accordance with the velocity of the transverse trolley 11 withouteffecting positional control of the transverse trolley 11/Q₂ and /R₂ areweighing matrices, wherein the first element is not equal to zero fromthe left in the weighing coefficient Q₂ relative to the trolleyposition, for a positional control type optimal-gain calculation mode inwhich the transverse trolley 11 is controlled so as to reach the targetposition. /Q₃ and /R₃ are weighing matrices, wherein the first andsecond elements are equal to zero from the left in the weighingcoefficient /Q₃ relative to the trolley position and velocity and thefirst element is set to a very large value from the left in the weighingcoefficient /R₃ relative to the trolley velocity command, for asway-damping type optimal-gain calculation mode in which the transversetrolley 11 is positioned and sway damping is effected by the sheaveblocks 14 and 15 alone.

The weighing matrices /Q₁, /R₁, /Q₂, /R₂ and /Q₃, /R₃ are represented bythe following matrices [21]:

Q₁=diag(0 q₂₁ q₃₁ q₄₁ q₅₁ q₆₁ q₇₁ q₈₁ q₉₁ q₁₀₁)

R₁=diag(r₁₁ r₂₁ r₃₁)

Q₂=diag(q₁₂ q₂₂ ₃₂ q₄₂ q₅₂ q₆₂ q₇₂ q₈₂ q₉₂ q₁₀₂)  [21]

R₂=diag(r₁₂ r₂₂ r₃₂)

Q₃=diag(0 0 q₃₃ q₄₃ q₅₃ q₆₃ q₇₃ q₈₃ q₉₃ q₁₀₃)

R₃=diag(∞r₂₃ r₃₃)

The weighing matrices /Q₁, /R₁, /Q₂, /R₂ and /Q₃, /R₃ composed of eachelement which means, in order from the left, in the same manner as q₁through q₁₀ and r₁ through r₃ described in 2) of (2) of the firstembodiment.

In fact, the first element ∞ of R₃ is indicative of a very large value.The elements, which are not designated as the value other than 0 or ∞,are adjusted by the actual machine test as described in 2) of (2) of thefirst embodiment.

(3) The selection of an optimal gain /K by theoperating-condition-classifying optimal-gain selecting unit 53 iscarried out as follows:

(a) If the load-piece stays far from the target place, the optimal gain/K₁ for the velocity following mode in which the operator effectsnotch-driving operation is selected as the optimal gain /K.

(b) If the load-piece is brought close to the target place, the optimalgain /K₂ for the positional control mode in which the transverse trolley11 is controlled so as to reach the target place is selected as theoptimal gain /K.

(c) If the load-piece is positioned at the target place, the optimalgain /K₃ for the sway-damping mode in which sway is damped by the sheaveblocks 14 and 15 alone is selected as the optimal gain /K.

(4) Then, in the same manner as in the first embodiment, the movingcondition quantities and the detection signals detected by the detectors31 through 38 and 40 are outputted to the controller 51.

(5) From the detection signals inputted, the controller 51 makes theoptimizing control unit 54 effect the calculation of the aforementionedequation [1] to determine the velocity command u₀ for the transversetrolley 11 and velocity commands u₁ and u₂ for respective sheave blocks14 and 15.

(6) Control command signals for velocity commands u₀, u₁ and u₂ areoutputted to the drivers 17, 18 and 19 for the transverse trolley 11 andthe two (left and right) sheave blocks 14 and 15 so as to drive them,whereby the hoisted load-piece 23 is optimally controlled to stopswinging.

FIG. 4 shows a control block representing a third embodiment of aswaying hoisted load-piece damping control apparatus of the presentinvention.

As shown in FIG. 4, in this embodiment, a controller 61 of the presentinvention is composed of an optimal-gain calculating unit 62 forindependently controlling transverse sway and skew sway in order tocalculate and supply optimal gains which are used when the transversetrolley and sheave blocks are driven for damping the transverse sway andskew sway, respectively, that is, when the transverse sway and skew swayare damped independently each from the other by separate drivers and anoptimizing control unit 63 for effecting sway-damping control based onthe optimal gain K determined by the resulting calculation in theoptimal-gain calculating unit 62 for independently controllingtransverse sway and skew sway. The optimizing control unit 63 is to,based on the optimal gain /K determined by the optimal-gain calculatingunit 62 for independently controlling transverse sway and skew sway inaccordance with the signal detected by the detectors 31 through 38 and40, drive the transverse trolley driver 17 for damping the transversesway and to drive the left and right sheave block drivers 18 and 19 fordamping the skew sway and thereby to effect the damping control.

Now, description will be made on a specific flow of sway damping by thecontroller 61 of this embodiment. (1) The optimal-gain calculating unit62 for independently controlling transverse sway and skew swaypreviously calculates an optimal gain in the following way:

1) In the state equation [16] shown above, if /x is substituted by/x=T/x′ to effect a mode transformation, then the following stateequation [22] can be obtained. Here, /x′ and /T indicate a new conditionquantity vector and a mode transforming matrix, respectively.$\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{^{\prime} = {{^{\prime}^{\prime}} + {^{\prime}}}} \\{where}\end{matrix} \\{^{\prime} = {{^{- 1}{}\quad ^{\prime}} = {^{- 1}}}}\end{matrix} \\{^{\prime} = \left\lbrack {x_{o}\quad x_{o}\quad x_{p}\quad x_{p}\quad x_{s}\quad x_{s}\quad d_{p}\quad d_{p}\quad d_{s}\quad d_{s}} \right\rbrack^{T}}\end{matrix} \\{ = \begin{bmatrix}1 & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & 1 & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & 1 & 0 & \quad & 1 & 0 & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & 0 & 1 & \quad & 0 & 1 & \quad & \quad & \quad & \quad & \quad & 0 \\\quad & \quad & 1 & 0 & \quad & {- 1} & 0 & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & 0 & 1 & 0 & \quad & {- 1} & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & 1 & 0 & \quad & 1 & 0 & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & 0 & 1 & \quad & 0 & 1 & \quad \\\quad & 0 & \quad & \quad & \quad & \quad & \quad & 1 & 0 & \quad & {- 1} & 0 & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & 0 & 1 & 0 & \quad & {- 1} & \quad\end{bmatrix}}\end{matrix} \right\} & \lbrack 22\rbrack\end{matrix}$

$x_{p} = \frac{x_{1} + x_{2}}{2}$

. . . displacement of center positions of the left and right sheaveblocks;${\overset{.}{x}}_{p} = \frac{{\overset{.}{x}}_{1} + {\overset{.}{x}}_{2}}{2}$

. . . velocity of center positions of the left and right sheave blocks;$x_{s} = \frac{x_{1} - x_{2}}{2}$

. . . difference of displacements of the left and right sheave blocks${\overset{.}{x}}_{s} = \frac{{\overset{.}{x}}_{1} - {\overset{.}{x}}_{2}}{2}$

. . . difference of velocities of the left and right sheave blocks$d_{p} = \frac{d_{1} + d_{2}}{2}$

. . . sway component of sway displacement${\overset{.}{d}}_{p} = \frac{{\overset{.}{d}}_{1} + {\overset{.}{d}}_{2}}{2}$

. . . sway component of sway velocity $d_{s} = \frac{d_{1} - d_{2}}{2}$

. . . skew component of sway displacement${\overset{.}{d}}_{s} = \frac{{\overset{.}{d}}_{1} - {\overset{.}{d}}_{2}}{2}$

. . . skew component of sway velocity

In one word, a new state equation is derived with respect to a newcondition quantity vector /x′ whose elements are composed of: x₀ and*x0: displacement and velocity of the transverse trolley 11; x_(p) and*x_(p): displacement and velocity of the center positions of the leftand right sheave blocks 14, 15; x_(s) and *x_(s): differences ofdisplacement and velocity of the left and right sheave blocks 14, 15;d_(p) and *d_(p): sway components of sway-displacement and sway velocityof the hoisted load-piece 23; and d_(s) and *d_(s): skew components ofsway displacement and sway velocity of the hoisted load-piece 23.

2) Next, an evaluation function J′ is determined. $\begin{matrix}\left. \begin{matrix}\begin{matrix}{J^{\prime} = {\int_{0}^{\infty}{\left( {{x^{\prime \quad T}Q^{\prime}x^{\prime}} + {u^{T}{Ru}}} \right)\quad {t}}}} \\{Q^{\prime} = {{diag}\left( {q_{1}^{\prime}\quad q_{2}^{\prime}\quad q_{3}^{\prime}\quad q_{4}^{\prime}\quad q_{5}^{\prime}\quad q_{6}^{\prime}\quad q_{7}^{\prime}\quad q_{8}^{\prime}\quad q_{9}^{\prime}\quad q_{10}^{\prime}} \right)}}\end{matrix} \\{R = {{diag}\left( {r_{1}\quad r_{2}\quad r_{3}} \right)}}\end{matrix} \right\} & \lbrack 23\rbrack\end{matrix}$

Weighing matrices Q′ and R are composed of each element which means asfollows:

q′₁, q′₂: weighing coefficients relative to the trolley position andvelocity;

q′₃, q′₄: weighing coefficients relative to the center positions andvelocities of the left and right sheave blocks;

q′₅, q′₆: weighing coefficients relative to the difference ofdisplacements and the difference of velocities of the left and rightsheave blocks;

q′₇, q′₈: weighing coefficients relative to the sway components of swaydisplacement and sway velocity;

q′₉, q′₁₀: weighing coefficients relative to the skew components of swaydisplacement and sway velocity;

r′₁: weighing coefficient relative to the trolley velocity command;

r′₂: weighing coefficient relative to the left sheave block velocitycommand; and

r′₃: weighing coefficient relative to the right sheave block velocitycommand.

3) Here, the optimal allocation of tasks to the transverse trolley andthe sheave blocks should be determined in order to achieve optimalcontrol of sway damping. This depends on the setup of the weighingmatrix /Q′ appearing in the above equation [23].

Sway of the hoisted load-piece 23 during the transverse travel comprisesa large transverse swinging motion, generated due to the inertia of thehoisted load-piece 23 when it is accelerated or retarded and a skewswinging motion relatively smaller than the transverse swinging motion,generated due to the eccentricity etc., of the hoisted load-piece 23. Inorder to damp the large transverse swinging motion, the transversetrolley 11 should be driven so as to effect sway damping since themovement of the sheave blocks 14, 15 is limited within a short stroke onthe transverse trolley 11 and therefore can not deal with the largeswinging motion. On the other hand, in order to damp the skew swingingmotion, the sheave blocks 14 and 15 should be driven so as to effectsway damping since the skew sway is relatively small and the movement ofthe transverse trolley 11 can not deal with this kind of motion,theoretically.

This allocation of tasks can be achieved by adjusting elements of theweighing matrix Q, specifically, q′₂, q′₄, q′₅ and q′₆ as follows.

The elements q′₃ and q′₄ are the weighing coefficients of the centerposition and velocity for the left and right sheave blocks 14, 15, andif these elements are taken large, the motion of center position of theleft and right sheave blocks 14 and 15 required for damping transverseswinging motion will be limited. Therefore, only the trolley 11 willcontribute to controlling the damping operation of transverse swingingmotion.

The elements q′₅ and q′₆ are the weighing coefficients of the differenceof displacement and the difference of velocity for the left and rightsheave blocks 14, 15, and if these elements are taken small, theopposite-direction movement of the left and right sheave blocks 14 and15 required for damping skew swinging motion can be secured within thestroke ranges of the sheave blocks 14 and 15. Further, since thetransverse trolley 11 cannot contribute to the damping of skew swingingmotion theoretically, only the sheave blocks will effectively controlthe damping operation of skew swinging motion.

The other elements of /Q′ and the elements of /R are adjusted by theactual machine test as described in 2) of (2) of the first embodiment.

4) On the basis of the aforementioned state equation [22], the optimalgain /K′ for minimizing the evaluation function [23] is determined bythe following equation [24]:

K′=−R⁻¹B′^(T)P′  [24]

where P represents the algebraic matrix Riccati's equation and is thepositively symmetric solution of the following equation [25]:

A′^(T)P′+P′A′−P′B′R⁻¹B′^(T)P′+Q′=0  [25]

On the other hand, the optimal gain /K′ is for a condition quantity /x′in which a mode transforming is effected. This is expressed by thefollowing equation [26]:

/K′/x′=/K′T⁻¹/x  [26]

The optimal gain /K for a condition quantity /x can be determined priorto the mode transformation by the following equation:

/K=/K′T⁻¹

(2) Then, in the same manner as in the first embodiment, the signalsdetected by the detectors 31 through 38 and 40 are outputted to thecontroller 61.

(3) From the signals inputted, the controller 61 makes the optimizingcontrol unit 63 effect the calculation of sway-damping optimizingcontrol based on the aforementioned equation [1] to determine thevelocity command u₀ for the transverse trolley 11 and velocity commandsu₁ and u₂ for respective (left and right) sheave blocks 14 and 15.

(4) Control command signals for velocity commands u₀, u₁ and u₂ areoutputted to the drivers 17, 18 and 19 for the transverse trolley 11 andthe two (left and right) sheave blocks 14 and 15, whereby the hoistedload-piece 23 is optimally controlled to stop swinging.

FIG. 5 shows a control block representing a fourth emrbodiment of aswaying hoisted load-piece damping control apparatus of the presentinvention.

As shown in FIG. 5, a controller 71 of this embodiment is has combinedfeatures of the controllers 51 and 62 described in the second and thirdembodiments.

Specifically, in the controller 71, an optimizing control unit 72, asreceiving detection signals from the detectors 31 through 38 and 40,sets up optimal controlling qualities referring to an optimal gain /Kfor operating condition classifying and for independently controllingtransverse sway and skew sway which is determined according to both theoperating condition and swinging modes (i.e., the transverse swingingmotion and the skew swinging motion) as executed in the controllers 51and 61 of the second and third embodiments. With the thus determinedoptimal controlling quantities, the controller 71 effects sway-dampingcontrol.

Now, description will be made on a specific sway-damping processeffected by the controller 71 of this embodiment.

In the optimal-gain calculating unit 62 for independently controllingtransverse sway and skew sway, an optimal gain is previously determinedin the following manner.

1) The state equation [22] is derived in the manner as in the thirdembodiment.

2) Next, evaluation functions J′₁ and J′₂ are set up as follows:$\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{J_{1}^{\prime} = {\int_{0}^{\infty}{\left( {{x^{\prime \quad T}Q_{1}^{\prime}\quad x^{\prime}} + {u^{T}R_{1}u}} \right)\quad {t}}}} \\{J_{2}^{\prime} = {\int_{0}^{\infty}{\left( {{x^{\prime \quad T}Q_{2}^{\prime}x^{\prime}} + {u^{T}R_{2}u}} \right)\quad {t}}}}\end{matrix} \\{Q_{1}^{\prime} = {{diag}\left( {0\quad q_{21}^{\prime}\quad q_{31}^{\prime}\quad q_{41}^{\prime}\quad q_{51}^{\prime}\quad q_{61}^{\prime}\quad q_{71}^{\prime}\quad q_{81}^{\prime}\quad q_{91}^{\prime}\quad q_{101}^{\prime}} \right)}}\end{matrix} \\{R_{1} = {{diag}\left( {r_{11}\quad r_{21}\quad r_{31}} \right)}}\end{matrix} \\{Q_{2}^{\prime} = {{diag}\left( {q_{12}^{\prime}\quad q_{22}^{\prime}\quad q_{32}^{\prime}\quad q_{42}^{\prime}\quad q_{52}^{\prime}\quad q_{62}^{\prime}\quad q_{72}^{\prime}\quad q_{82}^{\prime}\quad q_{92}^{\prime}\quad q_{102}^{\prime}} \right)}}\end{matrix} \\{R_{2} = {{diag}\left( {r_{12}\quad r_{22}\quad r_{32}} \right)}}\end{matrix} \right\} & \lbrack 27\rbrack\end{matrix}$

Weighing matrices /Q′1, /R1, /Q′2, /R2 are composed of each elementwhich, in order from the left, has the same meaning as q′₁ through q′₁₀and r₁ through r₃ described in 2) of (1) of the third embodiment.

Here, the optimal allocation of tasks to the transverse trolley and thesheave blocks should be determined in order to achieve optimal controlof sway damping. In the same manner described in 3) of (1) of the thirdembodiment, q′₃₁, q′₄₁, q′₅₁, q′₆₁, q′₃₂, q′₄₂, q′₅₂, q′₆₂ are set up soas to determine a weighing matrix for driving the transverse trolley andthe sheave blocks so as to damp the transverse sway and the skew sway,respectively, whereby effecting a control of damping sway.

Furthermore, as described in (2) of the second embodiment, the firstelement is equal to zero from the left of /Q′₁, and the first element isset to a value other than zero from the left of /Q′₁. In such a manner,/Q′₁ and /R₁ are set to velocity following type optimal-gain calculationmode weighing matrices. /Q′₂ and /R₂ are set to positional control typeoptimal-gain calculation mode weighing matrices.

The other elements are to be adjusted by the actual machine test asdescribed in 2) of (2) of the first embodiment.

3) On the basis of the state equation [22], the optimal gains /K′₁ and/K′₂ for minimizing the evaluation functions J′₁ and J′₂ represented bythe equation [27] are determined by the following equation [28]:$\begin{matrix}\left. \begin{matrix}{_{1}^{\prime} = {{- {\mathbb{R}}_{1}^{- 1}}^{\prime \quad T}{\mathbb{P}}_{1}^{\prime}}} \\{_{2}^{\prime} = {{- {\mathbb{R}}_{2}^{- 1}}^{\prime \quad T}{\mathbb{P}}_{2}^{\prime}}}\end{matrix} \right\} & \lbrack 28\rbrack\end{matrix}$

where /P₁′ and /P₂ represent the algebraic matrix Riccati's equationsand are the positively symmetric solutions of the following equation[29]: $\begin{matrix}\left. \begin{matrix}{{{^{\prime \quad T}{\mathbb{P}}_{1}^{\prime}} + {{\mathbb{P}}_{1}^{\prime}^{\prime}} - {{\mathbb{P}}_{1}^{\prime}^{\prime}{\mathbb{R}}_{1}^{- 1}^{\prime \quad T}{\mathbb{P}}_{1}^{\prime}} + {\mathbb{Q}}_{1}^{\prime}} = 0} \\{{{^{\prime \quad T}{\mathbb{P}}_{2}^{\prime}} + {{\mathbb{P}}_{2}^{\prime}^{\prime}} - {{\mathbb{P}}_{2}^{\prime}^{\prime}{\mathbb{R}}_{2}^{- 1}^{\prime \quad T}{\mathbb{P}}_{2}^{\prime}} + {\mathbb{Q}}_{2}^{\prime}} = 0}\end{matrix} \right\} & \lbrack 29\rbrack\end{matrix}$

On the other hand, the optimal gains /K₁ and /K₂ are for a conditionquantity /x′ in which the mode transforming is effected. This isexpressed by the following equation [30]:

/K′₁/x′=/K′₁T⁻¹/x, /K′₂/x′=/K′₂T⁻¹/x  [30]

The optimal gains /K′₁ and /K′₂ ¹ for a condition quantity /x can bedetermined prior to the mode transformation by the following equation:

/K₁=/K′₁T⁻¹, /K₂=/K′₂T⁻¹

Furthermore, an optimal gain /K₃, which allows the transverse trolley tostop for damping sway by the sheave blocks 14, 15 alone, is previouslydetermined in accordance with (2) of the second embodiment.

(2) The operating condition determining unit 52 determines operatingcondition of the transverse trolley 11 in the manner described in (1) ofthe second embodiment.

(3) The operating-condition-classifying optimal-gain selecting unit 53selects an optimal gain /K in the manner described in (3) of the secondembodiment.

(4) In the same manner as in the first embodiment, the detection signalsdetected by the detectors 31 through 38 and 40 are outputted to thecontroller 71.

(5) From the detection signals inputted, the controller 71 makes theoptimizing control unit 72 effect the calculation of the equation [1] todetermine the velocity command u₀ for the transverse trolley 11 andvelocity commands u₁ and u₂ for respective left and right sheave blocks14 and 15.

(6) Control command signals for velocity commands u₀, u₁ and u₂ areoutputted to the drivers 17, 18 and 19 for the transverse trolley 11 andthe left and right sheave blocks 14 and 15, whereby the hoistedload-piece 23 is optimally controlled to stop swinging.

As has been described in detail referring to the embodiments, the firstfeature of the swaying hoisted load-piece damping control apparatus ofthe present invention is equipped with a transverse trolley having apair of sheave blocks which are disposed on both sides of the transversetrolley and movable relative to the transverse trolley and furthercomprises: different kinds of detectors such as for detectingdisplacement and velocity of the transverse trolley, detecting swaydisplacement and velocity on right and left sides of the load-piece anddetecting moving condition quantities displacement and velocity of theright and left sheave blocks; a notch disposed on an operationcontrolling panel of the transverse trolley, for setting a trolleytransverse velocity by an operator; a transverse notch-driving controlquantity detector for outputting signals indicative of notch-drivingcontrol quantity (a trolley transverse velocity set value) which is setby operating the notch; and a controller for effecting sway-dampingcontrol of a load-piece hoisting device based on detection signalsobtained from the detectors, and is constructed such that the controllerhas an optimizing control unit which sets up optimal controllingquantities for the hoisted load-piece in accordance with the signalsdetected from the detectors, on the basis of a preset optimal gain forsway damping, and performs sway-damping control by driving thetransverse trolley and the sheave blocks by the setup optimalcontrolling quantities. Therefore, it is possible to establish easysway-damping control of the hoisted load piece in an assured manner byautomating the sway-damping control of the hoisted load-piece which hasbeen difficult in the prior art. Further, it is possible to realize theoptimal sway-damping control which can damp the sway of the hoistedload-piece as fast as possible and to inhibit the load-piece fromswinging. As a result, the work amount of the operator as well as thetime required for sway damping can be markedly decreased, thereby makingit possible to improve the conveying efficiency of hoisted load-pieces.

In accordance with the second feature of the swaying hoisted load-piecedamping control apparatus of the present invention, the controllercomprises: an operating condition determining unit which detects theoperating condition of the transverse trolley, based on thedisplacement, velocity and notch-driving control quantity for thetransverse trolley; an operating-condition-classifying optimal-gainselecting unit which, in accordance with the operating conditiondetected by the operating condition determining unit, selects anoperating-condition-classifying optimal gain for sway damping; and anoptimizing control unit which, based on the optimal gain outputted fromthe operating-condition-classifying optimal-gain selecting unit, sets upoptimal controlling quantities for the hoisted load-piece and performssway-damping control by driving the transverse trolley and the sheaveblocks in accordance with the setup optimal controlling quantities.Therefore, as described above, the work amount of the operator as wellas the time required for sway damping can be markedly decreased, therebymaking it possible to improve the conveying efficiency of hoistedload-pieces. In addition, during the transverse trolley travelstransversally, a velocity following type optimal control is effected sothat the transverse trolley quickly reacts to the operator's notchoperation, thereby allowing operability to be improved. During the stop,a positional control type optimal control is effected so that thehoisted load-piece does not pass but reaches the target position,thereby allowing safety to be improved. After the stop, an optimalcontrol for damping sway of the sheave blocks alone is effected so thatthe operator cab connected to the transverse trolley is not moved,thereby allowing the cab to be more comfortable.

In accordance with the third feature of the swaying hoisted load-piecedamping control apparatus of the present invention, the controllercomprises: an independently controlling optimal-gain calculating unitwhich drives the transverse trolley and the sheave blocks for dampingtransverse sway and skew sway, respectively, that is, calculatesindependent optimal gains used to control transverse sway and skew swayof the hoisted load-piece, independently one from the other by separatedrivers and outputs the calculated optimal gains; and an optimizingcontrol unit for effecting sway-damping control which, based on theoptimal gains outputted from the independently controlling optimal-gaincalculating unit, sets up optimal controlling quantities for hoistedload-piece and effects sway-damping control by driving the transversetrolley to damp transverse sway of the load-piece and driving the rightand left sheave blocks to damp skew sway of the load-piece. Therefore,as described above, the work amount of the operator as well as the timerequired for sway damping can be markedly decreased, thereby making itpossible to improve the conveying efficiency of hoisted load-pieces. Inaddition, for damping a large transverse sway caused during thetransverse travel, the sheave blocks are not driven since they are movedwithin short stroke ranges alone. Therefore, the transverse trolley isused for damping sway. Thus, during the transverse travel, the movementof the sheave blocks for damping skew swinging motion can be securedwithin the stroke ranges of the sheave blocks. Accordingly, during thetransverse travel, performance for damping skew sway is improved.

In accordance with the fourth feature of the swaying hoisted load-piecedamping control apparatus of the present invention, the controllercomprises: an independently controlling optimal-gain calculating unitwhich drives the transverse trolley and the sheave blocks for dampingtransverse sway and skew sway, respectively, that is, calculatesindependent optimal gains used to control transverse sway and skew swayof the hoisted load-piece, independently one from the other by separatedrivers and outputs the calculated optimal gains; an operating conditiondetermining unit which detects the operating condition of the transversetrolley, based on the displacement, velocity and notch-driving controlquantity; an operating-condition-classifying optimal-gain selecting unitwhich, in accordance with the operating condition detected by theoperating condition determining unit, selects a presetoperating-condition-classifying optimal gain or anoperating-condition-classifying optimal gain set up by the independentlycontrolling optimal-gain calculating unit and outputs the selected gain;and an optimizing control unit which, based on the optimal gainoutputted from the operating-condition-classifying optimal-gainselecting unit, sets up optimal controlling quantities for the hoistedload-piece and performs sway-damping control by driving the transversetrolley and the sheave blocks in accordance with the setup optimalcontrolling quantities. Therefore, as described above, the work amountof the operator as well as the time required for sway damping can bemarkedly decreased, thereby making it possible to improve the conveyingefficiency of hoisted load-pieces. In addition, during the transversetrolley travels transversally, a velocity following type optimal controlis effected so that the transverse trolley quickly reacts to theoperator's notch operation, thereby allowing operability to be improved.During the stop, a positional control type optimal control is effectedso that the hoisted load-piece does not pass but reaches the targetposition, thereby allowing safety to be improved. After the stop, anoptimal control for damping sway of the sheave blocks alone is effectedso that the operator cab connected to the transverse trolley is notmoved, thereby allowing the cab to be more comfortable. Furthermore, fordamping a large transverse sway caused during the transverse travel, thesheave blocks are not driven since they are moved within short strokeranges alone. Therefore, the transverse trolley is used for dampingsway. Thus, during the transverse travel, the movement of the sheaveblocks for damping skew swinging motion can be secured within the strokeranges of the sheave blocks. Accordingly, during the transverse travel,performance for damping skew sway is improved.

What is claimed is:
 1. A damping control apparatus for use in a devicefor hoisting a load-piece, said device having a transverse trolley beingtransversally movable and a driver thereof, and a pair of right and leftsheave blocks which are disposed along the moving directions of saidtransverse trolley and movable relative to said transverse trolley and adriver for each sheave block, said apparatus comprising: a trolleydisplacement detector for detecting a displacement of said transversetrolley; a trolley velocity detector for detecting a velocity of saidtrolley; a sway detector for detecting the displacement of a sway of theload-piece hoisted by said device; a sway velocity detector fordetecting the velocity of a sway of the load-piece hoisted by saiddevice; a sheave block displacement detector for detecting displacementof said right and left sheave blocks; a sheave block velocity detectorfor detecting velocity of said right and left sheave blocks; anoperation controlling panel and an operator velocity control disposed onsaid operation controlling panel of said device, allowing an operator toselect a setting for a trolley transverse velocity; a velocity settingdetector for outputting signals indicative of the operator's panelsetting for the trolley transverse velocity; a controller for effectingsway-damping control of said load-piece hoisting device based ondetection signals obtained from said detectors, said controller havingan optimizing control unit which sets up optimal controlling quantitiesfor the hoisted load-piece in accordance with the actual displacementand velocity detected by said trolley, sway, and sheave block velocityand displacement detectors, on the basis of a preset optimal gain forsway damping for the detected operator velocity setting, and performssway-damping control by driving said transverse trolley and said sheaveblocks through said drivers in accordance with the optimal controllingquantities; an operating condition determining unit which detects theoperating condition of said transverse trolley, based on thedisplacement and velocity and the notch-driving operation quantity forsaid transverse trolley; operating-condition-classifying optimal-gainselecting unit which, in accordance with the operating conditiondetected by said operating condition determining unit, selects anoperating-condition-classifying optimal gain for sway damping from aplurality of predetermined optimal gains; and an optimizing control unitwhich, based on the optimal gain outputted from saidoperating-condition-classifying optimal-gain selecting unit, sets upoptimal controlling quantities for the hoisted load-piece and performssway-damping control by driving said transverse trolley and said sheaveblocks in accordance with the setup optimal controlling quantities.